The French forward only signed for the Swans on a free transfer from Lyon over the summer, but has endured a frustrating spell at the Liberty Stadium so far.
Gomis has notched just one Premier League goal in the white shirt, with 12 of his 17 Premier League outings having been cameos from the bench.
But despite his struggles in South Wales, Arsene Wenger is understood to be considering a £6m swoop.
Swansea are believed to value their man at £6m, with any fee for the 29-year-old a profit following his free move.
However, the club may alter their stance, with Wilfried Bony’s long-awaited switch to Manchester City having now gone through.
Gomis is an experienced centre-forward having notched over 300 showings in French football and has also represented his nation on 12 occasions at senior international level.